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IPMAT Mock Test - 1 (New Pattern) - Commerce MCQ


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30 Questions MCQ Test IPMAT Mock Test Series - IPMAT Mock Test - 1 (New Pattern)

IPMAT Mock Test - 1 (New Pattern) for Commerce 2024 is part of IPMAT Mock Test Series preparation. The IPMAT Mock Test - 1 (New Pattern) questions and answers have been prepared according to the Commerce exam syllabus.The IPMAT Mock Test - 1 (New Pattern) MCQs are made for Commerce 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for IPMAT Mock Test - 1 (New Pattern) below.
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IPMAT Mock Test - 1 (New Pattern) - Question 1

If 2nC3 : nC3 = 17 : 2, find n.

Detailed Solution for IPMAT Mock Test - 1 (New Pattern) - Question 1
We know that

Given,

2nC3 : nC3 = 17 : 2

⇒ n = 26

Hence, the correct option is (B).

IPMAT Mock Test - 1 (New Pattern) - Question 2

The 9th term from the end in (x − 1 / x)12 is:

Detailed Solution for IPMAT Mock Test - 1 (New Pattern) - Question 2
ConceptWe have

General term: General term in the expansion of (x + y)n is given by

In the binomial expansion of (x + y)n, the rth term from end is (n − r + 2)th term.

Calculation:

We have to find 9th term from the end in (x − 1 / x)12

We know that rth term from end means (n − r + 2)th term from start.

So. 9th term from the end = [12 − 9 + 2]th term from start = 5th term from start

General term:

Hence, the correct option is (A).

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IPMAT Mock Test - 1 (New Pattern) - Question 3

The number obtained on rationalizing the denominator of is

Detailed Solution for IPMAT Mock Test - 1 (New Pattern) - Question 3
As we know,

Multiply and divide by √7 + 2

Hence, the correct option is (A).

IPMAT Mock Test - 1 (New Pattern) - Question 4

If , then x + y =

Detailed Solution for IPMAT Mock Test - 1 (New Pattern) - Question 4
As we know,

When two matrices are equal, all the corresponding elements must be equal.

Given,

Comparing two elements of first column,

2x + y = 7

⇒ y = 7 − 2x ...(1)

5x − 7 = y ...(2)

Comparing value of y from equation (1) and (2) we get,

7 − 2x = 5x - 7

⇒ 7 + 7 = 5x + 2x

⇒ 14 = 7x

∴ x = 2

Putting value of x in equation (1), we get

y = 7 − 2 × 2

⇒ y = 7 − 4

⇒ y = 3

Now,

x + y = 2 + 3 = 5

So, the value of x + y is 5.

Hence, the correct option is (C).

IPMAT Mock Test - 1 (New Pattern) - Question 5

A shopkeeper sells 200 shirts and makes a profit equal to the selling price of 25 shirts. Find his profit percentage.

Detailed Solution for IPMAT Mock Test - 1 (New Pattern) - Question 5
Given

A shopkeeper sells 200 shirts

Profit = S.P of 25 shirts

Formula:

C.P = S.P – Profit

Profit % = Profit / C.P × 100

Calculation:

Let S.P of 200 shirts be Rs. 200

S.P of 25 shirts = Rs. 25

Profit = S.P of 25 shirts = Rs. 25

C.P = Rs. 200 – Rs. 25 = Rs. 175

Profit % = 25 / 175 × 100

= 100 / 7%

= 14.28%

∴ The profit percentage is 14.28%

Hence, the correct option is (C).

IPMAT Mock Test - 1 (New Pattern) - Question 6

If m : n = 3 : 2, then (4m + 5n) : (4m − 5n) is equal to = ?

Detailed Solution for IPMAT Mock Test - 1 (New Pattern) - Question 6
Given

m : n = 3 : 2

= 11 : 1

Hence, the correct option is (C).

IPMAT Mock Test - 1 (New Pattern) - Question 7

Direction: Study the given bar graph carefully and answer the questions given below.

The following bar graph shows the number of Male and Female customers who visited a restaurant for 6 days of a week.

Q. What is the difference between the average number of Males and Females visiting the restaurant?

Detailed Solution for IPMAT Mock Test - 1 (New Pattern) - Question 7
Total number of males visiting the restaurant

= 120 + 75 + 80 + 135 + 125 + 75 = 610

Average number of males

= 610 / 6 = 101.67

Total number of Females visiting the restaurant

= 90 + 125 + 110 + 95 + 105 + 110 = 635

Average number of females

= 635 / 6 = 105.833

∴ Required difference = 105.83 − 101.67 = 4.16

Hence, the correct option is (D).

IPMAT Mock Test - 1 (New Pattern) - Question 8

Direction: Study the given bar graph carefully and answer the questions given below.

The following bar graph shows the number of Male and Female customers who visited a restaurant for 6 days of a week.

Q. What is the ratio between the number of Males visiting the restaurant on Tuesday, Thursday and Friday together and the number of females visiting the restaurant on the same days?

Detailed Solution for IPMAT Mock Test - 1 (New Pattern) - Question 8
Number of Males visiting the restaurant on Tuesday, Thursday and Friday

= 75 +135 + 125 = 335

Number of Females visiting the restaurant on Tuesday,

Thursday and Friday = 125 + 95 + 105 = 325

∴ Required ratio = 335 / 325 = 67 / 65 = 67 : 65

∴ The ratio between the number of Males visiting the restaurant on Tuesday, Thursday and Friday together and the number of females visiting the restaurant on the same days is 67 : 65.

Hence, the correct option is (C).

IPMAT Mock Test - 1 (New Pattern) - Question 9

Direction: Study the given bar graph carefully and answer the questions given below.

The following bar graph shows the number of Male and Female customers who visited a restaurant for 6 days of a week.

Q. Out of the total number of customers visiting the restaurant on Monday, Wednesday and Friday 40% have pre-booking of tables in the restaurant and the total number of customers visiting the restaurant on the remaining days 60% have pre-booked their tables. What is the sum of the customers who have pre-booking in the restaurant?

Detailed Solution for IPMAT Mock Test - 1 (New Pattern) - Question 9
Total customers on Monday, Wednesday and Friday

= 210 + 190 + 230 = 630

Customers who have pre-booking on Monday, Wednesday and Friday

= 40 / 100 × 630 = 252

Total customers on Tuesday, Thursday and Saturday = 200 + 230 + 185 = 615

Customers who have pre-booking on Monday, Wednesday and Friday

= 60 / 100 × 615 = 369

Required sum = 252 + 369 = 621

∴ The sum of the customers who have pre-booking in the restaurant is 621.

Hence, the correct option is (A).

IPMAT Mock Test - 1 (New Pattern) - Question 10

Direction: Study the given bar graph carefully and answer the questions given below.

The following bar graph shows the number of Male and Female customers who visited a restaurant for 6 days of a week.

Q. The number of customers visiting the restaurant on Sunday is 30% more than the number of customers visiting the restaurant on Wednesday and the ratio of male and female is 8 ∶ 5, then the number of males visiting the restaurant on Sunday is what percent of Males visiting the restaurant on Monday?

Detailed Solution for IPMAT Mock Test - 1 (New Pattern) - Question 10
Number of customers visiting the restaurant on Sunday

= 130 / 100 × (80 + 110)

= 13 × 19

= 247

Ratio of Male to females = 8 : 5

∴ Number of males on Sunday

= 8 / 13 × 247 = 152

Number of males on Monday = 120

∴ Required percentage

=152 / 120 × 100 = 126.67%

Hence, the correct option is (B).

IPMAT Mock Test - 1 (New Pattern) - Question 11

The value of x − yx−y when x = 2 and y = −2 is:

Detailed Solution for IPMAT Mock Test - 1 (New Pattern) - Question 11
Given,

x −yx−y

Here x = 2,y = −2

By substituting in x − yx−y we get,

x − yx−y = 2 − (−2)2 − (−2)

= 2 − (−2)2 + 2

= 2 − (−2)4

= 2 − (16)

= −14

The value of x − yx−y is −14.

Hence, the correct option is (D).

IPMAT Mock Test - 1 (New Pattern) - Question 12

The product of two numbers is 120 and the sum of their squares is 289. The sum of the two number is:

Detailed Solution for IPMAT Mock Test - 1 (New Pattern) - Question 12
Let the two number are a and b.

According to the question,

a2 + b2 = 289

ab = 120

(a + b)2 = a2 + b2 + 2ab

(a + b)2 = (289)2 + (2 × 120)

(a + b)2 = 529

(a + b) = 23

Hence, the correct option is (A).

IPMAT Mock Test - 1 (New Pattern) - Question 13

If x2 < 4 then the value of x is:

Detailed Solution for IPMAT Mock Test - 1 (New Pattern) - Question 13
Given,

x2 < 4

⇒ x2 − 4 < 0

⇒ (x − 2) × (x + 2) < 0

⇒ −2 < x < 2

⇒ x ∈ (−2, 2)

Hence, the correct option is (B).

IPMAT Mock Test - 1 (New Pattern) - Question 14

The average of some natural numbers is 15. If 30 is added to the first number and 5 is subtracted from the last number the average becomes 17.5 then the number of natural numbers is:

Detailed Solution for IPMAT Mock Test - 1 (New Pattern) - Question 14
According to the question, The average of some natural numbers is 15. If 30 is added to the first number and 5 is subtracted from the last number the average becomes 17.5 then the number of natural numbers is

Let the number of natural numbers be x

⇒ 15×x + 30 − 5 = 17.5×x

⇒ 15x + 25 = 17.5x

⇒ 2.5x = 25

⇒ x = 10

Hence, the correct option is (D).

IPMAT Mock Test - 1 (New Pattern) - Question 15

What is the value of =?

Detailed Solution for IPMAT Mock Test - 1 (New Pattern) - Question 15
Given

= 2

Hence, the correct option is (B).

IPMAT Mock Test - 1 (New Pattern) - Question 16

Find the nth term of the following sequence:

5 + 55 + 555 +….Tn

Detailed Solution for IPMAT Mock Test - 1 (New Pattern) - Question 16
We will it through option checking method

5/9 × (10n − 1)

We put n = 1,

It means Option C is satisfying the sequence so the nth term would be

= 5/9 × (10n − 1)

Hence, the correct option is (C).

IPMAT Mock Test - 1 (New Pattern) - Question 17

Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:

Detailed Solution for IPMAT Mock Test - 1 (New Pattern) - Question 17
Let the speeds of the two trains be x m/sec

and y m/sec respectively.

Then, length of the first train = 27x metres,

and length of the second train = 17y metres.

∴ 27x + 17y / x + y = 23

⇒ 27x + 17y = 23x + 23y

⇒ 4x = 6y

⇒ x/y = 32

Hence, the correct option is (B).

IPMAT Mock Test - 1 (New Pattern) - Question 18

Which one of the following is an example of the empty set?

Detailed Solution for IPMAT Mock Test - 1 (New Pattern) - Question 18
The empty set is the unique set having no elements; the count of elements in a set is zero.

{x : x is a common point to any two parallel lines}

So, it is an empty set as parallel lines do not have a common point.

Set of all even prime number = {2}

Thus, its not empty set.

{x : x2 − 2 = 0 and x is a real number }

x = +2 and −2

So, its not empty set.

{x:x is a natural number, x>8 and simultaneously x < 12}

Thus, it is also non empty set.

Hence, the correct option is (D).

IPMAT Mock Test - 1 (New Pattern) - Question 19

The first term of an Arithmetic Progression is 22 and the last term is −11. If the sum is 66, the number of terms in the sequence are:

Detailed Solution for IPMAT Mock Test - 1 (New Pattern) - Question 19
Number of terms = n (let)

First term (a) =22

Last term (I) =−11

Sum =66

Sum of an AP is given by:

= Number of terms × First term + Last term / 2

n = 12

No. of terms = 12

Hence, the correct option is (B).

IPMAT Mock Test - 1 (New Pattern) - Question 20

What is the value of 1/2 log1025 –2log103 + log1018?

Detailed Solution for IPMAT Mock Test - 1 (New Pattern) - Question 20

1/2 log1025 –2log103 + log1018

Hence, the correct option is (C).

IPMAT Mock Test - 1 (New Pattern) - Question 21

A sum of money becomes 5 times at simple interest in 16 years. What is the rate of interest?

Detailed Solution for IPMAT Mock Test - 1 (New Pattern) - Question 21
Given

The Sum of money becomes 5 times of itself in 16 years

Formula used:

(i) SI = PRT / 100

Where P = principal

R = rate

T = time

(ii) A = SI + P

Where, A = Amount

SI = simple interest

Let the principal be P.

For 16 years,

SI = (P × R × 16) / 100

= 16PR / 100

A = SI + P

⇒ 5P = 16PR / 100 + P

⇒ 4P = 16PR / 100

⇒ R = 400 / 16

⇒ R = 25%

∴ The rate of interest is 25%.

Hence, the correct option is (B).

IPMAT Mock Test - 1 (New Pattern) - Question 22

If x2 − 2pxy − y2 = 0 and x2 − 2qxy − y2 = 0 bisect angles between each other, then:

Detailed Solution for IPMAT Mock Test - 1 (New Pattern) - Question 22
Equation of angle bisector for ax2 + 2hxy + by2 = 0 is

x2 − y2a − b = xy/h

For x2 − 2pxy − y2 = 0, equation of angle bisector will be

⇒ x2 − y2 / 1 − (−1) = xy / − p

⇒ x2 − y2 + 2xy / p = 0 .....(i)

Given equation of angle bisector is:

x2 − 2qxy + y2 = 0 .....(ii)

Comparing both the equations:

⇒ 2 / p = −2q

⇒ pq = −1

⇒ pq + 1 = 0

Hence, the correct option is (C).

IPMAT Mock Test - 1 (New Pattern) - Question 23

If A = {1, 4}, B = {2, 3}, C = {3, 5} then (A × B) ∩ (A × C) is equal to:

Detailed Solution for IPMAT Mock Test - 1 (New Pattern) - Question 23
Given: A = {1, 4}, B = {2, 3}, C = {3, 5}

Here, we have to find (A × B) ∩ (A × C)

As we know that, A × B = {(a, b) ∣ a ∈ A and b ∈ B}

⇒ A × B = {(1, 2), (1, 3), (4, 2), (4, 3)} ......(i)

⇒ A × C = {(1, 3), (1,5 ), (4, 3), (4, 5)} ......(ii)

From (i) and (ii) we can say that,

⇒ (A × B) ∩ (A × C) = {(1, 3), (4, 3)}

Hence, the correct option is (A).

IPMAT Mock Test - 1 (New Pattern) - Question 24

The value of 51/4 × (125)0.25 is =?

Detailed Solution for IPMAT Mock Test - 1 (New Pattern) - Question 24

Given:

51/4 × (125)0.25

= 50.25 × (53)0.25

= 50.25 × 5(3×0.25)

= 50.25 × 50.75

= 5(0.25 + 0.75)

= 51

= 5

Hence, the correct option is (B)

IPMAT Mock Test - 1 (New Pattern) - Question 25

Find the remainder when 6799 is divided by 7.

Detailed Solution for IPMAT Mock Test - 1 (New Pattern) - Question 25
Remainder of 6799 /7

or,

63 is divisible by 7 for any power, so required remainder will depend on the power of 4

Required remainder

Note :

4+/7 remainder = 4

If we check for more power we will find that the remainder start repeating themselves as 4, 2, 1, 4, 2, 1 and so on. So when we get A number having greater power and to be divided by the other number B, we will break power in (4n + x) and the final remainder will depend on x i.e.

Ax / B.

Hence, the correct option is (C).

IPMAT Mock Test - 1 (New Pattern) - Question 26

Which of the following is not a finite set?

Detailed Solution for IPMAT Mock Test - 1 (New Pattern) - Question 26
A set that has the finite number of elements is said to be a finite set.

Option (D): {x ∈ N : x is even}

As we can see that, elements of {x∈N:x is even} are: 2, 4, 6, 8,…….

So, there are infinitely many elements in the set {x∈N:x is even}

Thus, {x ∈ N : x is even } is not a finite set.

Option (A) {x : x ∈ N and x2 < 36}

As we can see that, elements of {x:x∈N and x2 < 36} are: 1,2,3,4,5

So, there are 5 elements in the set {x:x∈N and x2 < 36}

Thus, the set {x : x ∈ N and x2 < 36} is a finite set.

Option (B): {x ∈ z : 0 < x < 10}

As we can see that, elements of {x ∈ z : 0 < x < 10} are: 1, 2, 3,………,9

So, there are 9 elements in the set {x ∈ z : 0 < x < 10}

Thus, the set {x ∈ z : 0 < x < 10} is a finite set.

Option (C): {x : x ∈ N and x2 = x}

∵ x2 = x

⇒ x2 − x = 0

⇒ x(x − 1) = 0

⇒ x = 0 or 1

But since x∈N.

So, x = 0 ∉ {x : x ∈ N and x2 = x}

Therefore, only x = 1 ∈ {x : x ∈ N and x2 = x}

Thus, {x : x ∈ N and x2 = x} is a finite set.

Hence, the correct option is (D).

IPMAT Mock Test - 1 (New Pattern) - Question 27

The relation R on the set of integer is given by R = {(a, b) : a − b is divisible by 7, where a, b ∈ Z}, then R is a/an:

Detailed Solution for IPMAT Mock Test - 1 (New Pattern) - Question 27
Given that

R is a relation on Z and is defined as:

R = {(a, b) : a − b is divisible by 7 where a, b ∈ Z}

We know that:

A relation R on a set A is said to be an equivalence relation if R is reflexive, symmetric and transitive.

Therefore,

R is reflexive as:

a − a = 0 is divisible by 7 for all a ∈ Z.

Suppose, if (a, b) ∈ R

⇒ 7 divides a − b i.e.,

⇒ a − b = 7m, where m ∈ Z

⇒ b−a = 7n, where n = −m

⇒ 7 divides b−a too, which implies that:

(b, a) ∈ R.

Therefore, R is symmetric.

Suppose, if (a, b) ∈ R and (b, c) ∈ R, then:

a − b and b − c are divisible by 7.

⇒ a − b = 7m and b − c = 7n, where m, n ∈ Z

⇒ a − c = 7q, where q = m + n

⇒ (a, c) ∈ R

Therefore, R is transitive.

Hence, the correct option is (D).

IPMAT Mock Test - 1 (New Pattern) - Question 28

The distance between two points A and B is 600 km. When they start moving towards each other they meet in 12 hours. If A started moving 5 hours after B, then they meet in 10 hours. Taking these into account find the speed of B.

Detailed Solution for IPMAT Mock Test - 1 (New Pattern) - Question 28
Given

Distance between A and B = 600 km

Time taken to meet each other (when they start together) = 12 hours

Distance = Speed × Time

Relative speed of two bodies when they travel towards each other = Sum of their speed

When they start moving towards each other, they meet in 12 hours,

Let the speed of A be ‘A’ km/hr and the speed of B be ‘B’ km/hr

⇒ 600 / (A + B) = 12

⇒ A + B = 50......(1)

If A started moving 5 hours after B, then they meet in 10 hours,

Distance covered by A and B in 10 hours = 50 × 10 = 500

Remaining distance (600 - 500 = 100 km) was already covered by B in 5 hours

Speed of B = 100 / 5 = 20 km/hr

∴ The speed of B is 20 km/hr

Hence, the correct option is (A).

IPMAT Mock Test - 1 (New Pattern) - Question 29

Order of is

Detailed Solution for IPMAT Mock Test - 1 (New Pattern) - Question 29
Given,

First matrix =

Number of rows (m1) = 2

Number of columns (n1) = 3

So, order of first matrix = 2 × 3

And second matrix =

Number of rows (m2) = 3

Number of columns (n2) = 1

So, order of first matrix = 3 × 1

As we know,

Multiplication of matrices is possible if

Number of column (n1) in the first matrix = Number of rows (m2) in the second matrix

i.e., n1 = m2

∴n1 = m2 = 3

So, is possible.

As we know,

Multiplication of matrices is possible if the order of the new matrix is a row of the first matrix and column of the second matrix.

i.e., m1 × n2

Now,

Order of new matrix formed by multiplication = m1 × n2 = 2×1

Hence, the correct option is (B).

IPMAT Mock Test - 1 (New Pattern) - Question 30

car covers a distance of 4 km in 6 minutes. If it's speed is decreased by 2 km/hr, then find the time taken by the car to cover same distance.

Detailed Solution for IPMAT Mock Test - 1 (New Pattern) - Question 30
Given

Distance = 4 km

Time = 6 minutes

Distance = Speed × Time

Speed = Distance / Time

Time = 6 minutes

⇒ Time = ( 6/60) hr = (1/10) hr

⇒ Speed = DistanceTime = 4(1/10)

⇒ Speed = 40 km/hr

According to the question,

If its speed is decreased by 2 km/hr

⇒ New speed = (40 - 2) km/hr = 38 km/hr

Time taken by the car to cover same distance,

Time = Distance / Speed

⇒ Time = (4/38) hr = (4/38) × 60 = 120/19 minutes

∴ The time taken by the car to cover same distance is 120/19 minutes.

Hence, the correct option is (A).

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